A new control chart to monitor mean shifts of bi-variate quality control processes

We propose a new approach to monitor an overall mean shift of a bi-variate quality control system. To do this, we first define beliefs on deciding whether the quality characteristics are in out-of-control state. Then, by taking new observations, in an iterative approach we update the belief of each quality characteristics being out-of-control. This task is performed using a recursive method and prior beliefs. Finally, we introduce a statistics in combination with Bivariate Exponentially Weighted Moving Average(BEWMA) statistics to improve the performance of the proposed method. In order to understand the proposed methodology and to evaluate its performance, we perform a simulation study. Moreover, we compare in- and out-of-control average run lengths of the proposed method with the ones from the well-known MCUSUM and MEWMA procedures in different scenarios of mean shifts. The results of the simulation study show that the proposed methodology performs better than the other methods for small shifts of the process mean.